Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

Original languageEnglish (US)
Title of host publicationMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
PublisherAmerican Nuclear Society
Pages1327-1338
Number of pages12
Volume2
ISBN (Print)9781510808041
StatePublished - 2015
EventMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 - Nashville, United States
Duration: Apr 19 2015Apr 23 2015

Other

OtherMathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
CountryUnited States
CityNashville
Period4/19/154/23/15

Keywords

  • Anisotropic scattering
  • Convergence acceleration
  • Diagonalization
  • Second order ODE

ASJC Scopus subject areas

  • Mathematics(all)
  • Nuclear and High Energy Physics

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  • Cite this

    Ganapol, B. D. (2015). Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation. In Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 (Vol. 2, pp. 1327-1338). American Nuclear Society.